BABAR & KANGA,
on the Search for µ-µ’s
Samantha Hamernik
Hastings College – Iowa State University
2 August 2002
No, I’m not talking about the King of Elephants; I’m talking about the King of Bfactories and a detector named BABAR at the Stanford Linear Accelerator Center (SLAC) in
Palo Alto, CA. SLAC is the base camp of B-physics for approximately 600 physicists and
engineers from 76 institutions in 9 countries and it became my virtual home for the summer,
via Ames, IA. Knowing little or nothing about high-energy physics at the onset of the
summer I did what all head-strong undergraduates would do, I set out to defy the Standard
Model of Fundamental Particles and Interactions (SM). Again, I didn’t know this at the
beginning of the summer, but a B0 meson is not supposed to decay to a muon (µ) and a tau(τ),
so if it does and we find it… as my mentor, Jim Cochran would say, “It’s a trip to
Stockholm!” This analysis is far from Nobel quality, so far, but for the last 10 weeks I have
set out in search of µ-µ’s with BABAR, KANGA, and even ROOT.
The name BABAR comes from this detector serving as a B-factory, where B and B-bar
mesons are produced. The B particle mentioned is one of about 260 known hadrons, which
are combinations of quarks that can be either baryons (three quarks) or mesons (two quarks).
B mesons consist of a d-quark and a b-antiquark while the opposite is true for the B meson’s
antiparticle, B-bar. The mesons come about from the decay of an upsilon (4S) resonance
produced in the collision of the PEP-II storage ring’s electrons and positrons. A vast amount
of collisions are needed since interesting events come along only every 100-1000 collisions.
Figure 1: This electron-positron collision illustrates how B and anti-B mesons are produced.
2
The millions of B meson pairs needed for this experiment are produced by collisions
within the PEP-II storage ring. This ring has one high-energy beam, 9 GeV electrons, and one
low-energy beam, 3.1 GeV positrons, in the opposite direction. The asymmetric collision
creating an upsilon (4S) creates a time dependence that is very useful for studies of CP
(charge and parity) violation, but is not needed for this analysis.
Figure 2: Here is a diagram of PEP II with the BABAR detector.
The decay modes of the B pairs are “seen” and recorded by the BABAR detector. The
BABAR detector consists of six layers working together to provide particle tracking and
identification. The Silicon Vertex Tracker (SVT), being closest to the collision serves as the
only detection source for very low energy particles and delivers position information about all
particles passing though it. The Drift Chamber, surrounding the SVT, is filled with heliumbased gas and measures momentum of charged particles and energy loss. The DIRC,
Detector of Internally Reflected Cherenkov light, searches for charged hadrons. The fourth
layer is the Caesium Iodide Electromagnetic Calorimeter (EMC) that provides energy loss
data, neutral hadron information, and electron identification down to 0.5 GeV. Outside of the
EMC is a super-conducting coil with a 1.5 Tesla solenoidal magnetic field to curve the tracks
of charged particles. The last layer of the detector, the Instrumented Flux Return, is
especially important to the analysis presented here because it is used for muon identification
down to 0.6 GeV. [1]
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Just as experiments in any discipline of science, BABAR is used as a tool to better
understand what we think we know and search for new science. New physics by definition is
on the frontier of discovery and in elementary particle physics it serves as a means of defying
or adding to the SM. Just as classical physics has laws of conservation (energy, momentum,
etc.), the SM has laws of conservation that govern behavior and decays of particles.
Conservation of lepton type number is what this analysis is concerned with. Lepton number
is a way to keep track of what types of particles are present in a decay. There are three lepton
number categories corresponding to the three known generations of matter: electron-type (e),
muon-type (µ), and tau-type (τ). Leptons (electrons, muons, taus and their matching
neutrinos) are assigned a lepton number of one in their respective type while their
antiparticles are assigned a number of negative one in that type. Particles not belonging to a
certain family have a lepton number of zero in that family, i.e. muons would have an electron
number of zero. With these numbers assigned to particles on either side of a decay the SM
says that lepton number of each type should be conserved, respectively. As you can see the
electron, muon, and tau numbers are all individually conserved in this modeled decay.
µ
elect. #
muon #
tau #
muon
0
1
0
Æ
νµ
+
e-
+ ν-bar e
mu neut.
electron
e anti-neut.
=
0
+
1
+
-1
=
1
+
0
+
0
=
0
+
0
+
0
Figure 3: An example of lepton type number conservation
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In contrast, here is the B0 decay that is part of the signal event of this analysis and is
currently not allowed by the SM. Muon and tau numbers are not conserved here and would
call for new physics if found.
Β0 Æ τ
elect. #
muon #
tau #
B0
0
0
0
=
U
U
+ µ
tau
muon
0 + 0
0 + 1
1 + 0
Figure 4: The decay in this analysis that does not conserve lepton number.
Lepton number has not been broken yet, but theorists are working on ways to explain
these types of decays if they are found. Two such theories are that of Flavor Changing
Neutral Currents (FCNC) and Leptoquarks (LQ). [2,3] I have included Feynman diagrams of
each to illustrate. Shown on the left is a theoretical FCNC that decays a B0 meson into two
opposite sign leptons. On the right is a LQ that also demonstrates lepton mixing. With the
recent evidence of neutrino mass, lepton mixing is no longer strictly forbidden.
µ+
B0
B0
FCNC
_______
LQ
τ-
Figure 5: Flavor changing neutral current decay
µ+
τFigure 6: Leptoquark decay
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In order to defy or add to the Standard Model unusual and yet unseen decay modes
must be explored, and that is exactly what my analysis utilizes. A group at CLEO (Cornell
University) published a paper on this exact signal decay in 1994. [4] Their branching fraction
was given as B(B0Ƶτ) < 8.4 x 10-4 with a 90% confidence level and they approached the
analysis with taus decaying to high momentum pions. A sub-group of the lepton BC analysis
working group has been studying B0 Æ l+l- [5] for 1 1/2 years, but their emphasis has not yet
been on final state µ+µ− events like mine. My faculty mentor, Jim Cochran, is a member of
that group and is working on the parallel analysis with a final state of e+e-. His groundwork
served as a very much needed and appreciated catalyst for my own analysis and my work
served as a useful crosscheck and supplement to his. The diagram below shows our ideal
decay with a final state of two opposite sign muons and undetected τ and µ neutrinos.
Muon1 +/-
B0
9 GeV e-
Ups(4S)
Muon 2 -/+
Tau -/+
µ
neutrino
τ
neutrino
3.1 GeV e+
B0-bar
Figure 7: This is a diagram of a possible decay of the signal event in this analysis.
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The method in which I went about my search for µ−µ’s starts with a lot of C++ code.
BABAR’s internal computing/software framework is powerful and flexible to allow the user to
focus on optimizing the tools for their analysis. The analysis/reconstruction framework
provides over two million lines of code that may be accessed with each analysis. Another
asset of collaboration work is that you are encouraged to look at other user’s code to help you
along. Once your analysis is in working order you run it over signal Monte Carlo (MC),
which is a simulation of what you are searching for. You also run your code over simulated
backgrounds, which are events similar to your signal, that may be mistaken for signal with
respect to certain variables. An important part of this process is blind analysis that prevents a
user from being biased towards a certain experimental outcome. In blind analysis you do not
look at the signal box of your data until the analysis has been finalized and are systematics
understood. BABAR detector events (signal and backgrounds, real and MC) that the analysis
code is run over are stored in KANGA. KANGA (Kinder ANd Gentler Analysis) is a means
of storing data that makes it more accessible to users than the BABAR Objectivity database.
BABAR has the largest publicly known database with more than 500 Terabytes.
Code written for analysis collects information on a number of variables. By setting
criteria early on in your code, you can regulate what types of events you explore and which
ones are tossed out. For example, in my code only events with two possible muons are further
investigated. I say possible muons because they are initially identified as muons, but could
actually be pions or D* mesons. After an event has been recognized as possibly having two
muons in it twenty-three variables are checked and stored in ntuples (lists of variables) to be
later used in ROOT graphical analysis.
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One of the later sections of my code stores truth information, which contains the
generated particle identification of the Monte Carlo events. This lets me know if my
“possible” muons are “real” muons. Within the truth section I also created a large conditional
that checks the parentage of my final state muons. Parentage simply traces back where
particles come from, like their mother and grandmother. In my signal events there are only
four possible decays, differing only in charge. With a truth lineage check it is possible to flag
an event as true signal only if it fits in one of these four decays exactly. Here is an example of
output from an event that was true signal.
EvtCounter: processing event # 13 [ 1d:ffffffff:000065/c2f8cc75:S ]
m1tag p(), charge: 2.48691 1
m2tag p(), charge: 1.7842 -1
After Boost...
m1tagCM p(), charge: 2.46962 1
m2tagCM p(), charge: 1.11307 -1
m1tag truth id: mu+
m1tag truth p(): 2.46254
m1tag theMother id: anti-B0
m1 granny : Upsilon(4S)
m2tag truth id: mum2tag truth p(): 1.91018
m2tag theMother id: taum2 granny : anti-B0
Muon1
M1mom
Muon2
mu_plus
anti_B0
mu_minus
trk overlaps with elec - not appending to restOfEvent
-2.30224 0.695336 0.633162 2.49082
trk overlaps with elec - not appending to restOfEvent
0.600862 -0.0521649 1.67917 1.78965
Mllmis = 5.24706
roe thrust axis: 0.742691 -0.669411 0.0173019
Bthr thrust axis: 0.864684 -0.221186 0.450998
cosThetaT: 0.79806
|cosThetaT|: 0.79806
Fox Wolfram ratio, R2 = 0.28189
Charge List Length 10
Neutral List Length 7
Muon List Length 3
Electron List Length 0
Good events(doublemuons):1
Truth good events (honestmumupairs):1
Fraction of truth pairs to total pairs :1
M2mom
tau_minus
M2granny
anti_B0
Figure 8: Here is an actual output of an event passing selection criteria.
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As mentioned before, all of these values are also put into ntuples for later graphical
analysis. When you plot distributions of certain variables you hope there will be a difference
in what your signal and background plots look like. These differences are what you exploit
when making cuts on your data. By only allowing events with more strict criteria into the mix
for plots you can reduce the background and keep as much signal as possible to increase your
chances of seeing the actual events you are looking for. The variables I choose to plot and
their first pass cuts are listed.
Variable
Allowed region
Description
µ1_p
(2.2 ÅÆ2.5 GeV/c)
Momentum of the muon from the original B0 decay
µ2_p
(1.2 ÅÆ1.5 GeV/c)
Momentum of the second muon from the tau decay
Mistot
(1.4 ÅÆ 2.0 GeV/c)
Missing energy that would be attributed to neutrinos
µ2 mistot
(1.8 ÅÆ 3.0 GeV/c)
Absolute value of the vector sum of µ2_p and mistot
R2
(0.2 ÅÆ 0.3)
Ratio between the 2nd & 0th Fox Wolfram moments
| cos θ |
(0.0 ÅÆ 0.8)
Theta is the angle between the lepton pair direction
and the thrust axis of the rest of the event
Mllmis
(5.2 ÅÆ 5.28 GeV/c2) Beam constrained invariant mass
∆E
(-0.75 ÅÆ 0.25 GeV) The change in energy of the system
________________________________________________________________________
Figure 9: This is a list of the variables plotted and cut upon to reduce background.
The next six pages are my initial plots with only a parentage cut on the signal (top left
corner). The gray vertical lines indicate my first cuts. Even though the y-axis shows number
of events, it is arbitrary because at this stage we are looking only for differences in shape.
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µ1Momentum
Figure 10: The strong definition of this signal peak shows that µ2 momentum is an excellent variable to cut on.
By keeping the data between the vertical lines we can pass a large percentage of signal and cut out a
lot of the background data.
10
µ2Momentum
Figure 11: As you can see µ2 momentum is not the best variable to cut on because of the wideness of the signal.
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Mistot
Figure 12: Mistot is also not a strong variable to cut on because too much signal is lost.
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µ2mistot
Figure 13: The combined variable of µ2 momentum and mistot is much easier and more efficient to cut on
because if it’s well defined peak .
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R2
Figure 14: R2 is most efficient for reducing eetautau background(bottom right), eliminating almost all of it.
14
15
|cos θ|
Figure 15: As can be expected the cosine θ is spread pretty evenly from 0-1 and is not a great cutting variable.
16
Mllmis
Figure 16: The invariant mass, mllmis, also serves as a strong cut.
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∆E
Figure 17: ∆E is the last strong cut with a very well defined peak in respect to the backgrounds.
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Calculations from these first pass cuts are shown below. In using ROOT, I was only able to
set so many variable criteria at one time so I broke my cuts into two, hopefully uncorrelated,
sections. Muon 1 momentum, muon 2 momentum, mistot and muon2mistot selections are in the
first cut while R2, |cos θ|, mllmis, and ∆E are in the second.
Sample
signal
B+B- generic
B0B0bar generic
e+e- -> ccbar
e+e- -> uds
e+e- -> tau+tau-
Original cut 1
1574 104
894225 328
220048
87
220870 128
21864
9
398088 1893
+/- cut 2
10 202
18 2717
9 774
11 290
3
25
44
67
+/14
52
28
17
5
8
cut 1 %
6.61%
0.04%
0.04%
0.06%
0.04%
0.48%
+/- cut 2 %
0.65% 12.83%
0.00% 0.30%
0.00% 0.35%
0.01% 0.13%
0.01% 0.11%
0.01% 0.02%
+/0.90%
0.01%
0.01%
0.01%
0.02%
0.00%
Figure 18: From this spreadsheet you can see the original number as well as the number
passing and percentages left after each cut. Errors were determined by square roots.
In order to calculate the final percentage passing we multiply our cuts. From this we can see
that after such cuts we are left with a final signal efficiency of 0.85%. Our backgrounds are
determined from the equation:
Nbkg = σ ε L
In this equation, σ is the cross-section, ε is the efficiency (%), and L is luminosity. With
100 fb-1 (inverse femto-barns, 1 fb = 1015 barns, 1 barn = 10-24 cm) of data we see that we expect
about 402 background events. This number is extremely high and we hope to cut it down to one or
two events before unblinding can happen.
ε
Sample
signal
B+B- generic
B0B0bar generic
e+e- --> ccbar
e+e- --> uds
e+e- --> tau+tau-
% final
0.8480%
0.0001%
0.0001%
0.0001%
0.0000%
0.0001%
σ [nb] σ [fb]
+/0.0059%
0.0000%
0.0000%
0.0000%
0.0000%
0.0000%
nb
0.525
0.525
1.3
2.09
0.91
fb
L
[fb-1]
Nbkg
525000
100
525000
100
1300000
100
2090000
100
910000
100
Total Nbkg
58.5
73.0
98.9
98.4
72.8
401.6
Figure 19: Here is the calculation of final percentage and background events in 100 fb-1.
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In conclusion, this analysis is far from over. With only ten weeks of work I have learned
enough about high-energy physics to adapt and write analysis code to search for a
B0 Æ µ τ, τ Æ νµ + ντ + µ signal event. A first pass of signal and background has been
accomplished and initial cuts have been applied. Through graphical analysis it is evident that µ1
momentum, µ2mistot, mllmis, and ∆E are the strongest variables to apply cuts to for reducing
background and salvaging as much signal as possible. Even though the cuts are far from tight
enough, yet, they are in place and easily strengthened. This analysis has a long way to go before it
is to the point of unblinding, but it has served as an excellent learning experience for myself.
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References:
[1]
BABAR Collaboration, “The BABAR Physics Book”, edited by P.F. Harrison and
H.R. Quinn (1998).
[2]
M. Gronan and D. London, Physical Review D 55, 2845 (1997).
[3]
J. Pati and A. Salam, Physical Review D 10, 275 (1974).
[4]
R. Ammar et al., Physical Review D 49, 11 (1994).
[5]
J. Cochran, S. Yang, and V. Halyo, “Search for B0 Æ l+l- “, BABAR Analysis
Document #322. (2002).
Acknowledgments:
I would like to thank Dr. Steve Kawaler in the ISU astronomy department for passing me
over so that I could work with my high-energy mentor, Dr. Jim Cochran. Jim, you were fabulous
and have given me amazing insight in a field I knew nothing about. Thank you. I’ll mention you
again in my Nobel Prize acceptance speech. I would also like to thank the National Science
Foundation, Iowa State University, and Dr. Marzia Rosati for coordinating projects like these and
giving undergraduates the opportunity to experience research science firsthand.
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